A set of operators, which act on the eigenstates of the atomic Hamiltonian in the presence of a partial I-J decoupling in a way analogous to the way the usual irreducible tensor operators act on the eigenstates of the total angular momentum, is introduced. Starting from these operators a set of operators, analogous to Haroche's pseudotensor operators, is obtained for the dressed-atom Hilbert space. They are thus particularly suitable to the theoretical treatment of the Delta mF>1 multiple quantum transitions within the Zeeman levels of a hyperfine state of an alkali atom. As an example, this treatment is applied to a system having a 'fictitious' spin F=1, and it is shown that the contribution of the single and multiple quantum transitions to the multipole components of the dressed-atom density matrix is separated.